Question

Oblicz długości odcinków x,y,z.

Answer 1

1)

ctg30 = 6√3/ a

ctg(30+15) = 6√3/b

x = b-a

 

√3 = 6√3/a 

a= 6√3/√3

a=6

 

ctg45= 6√3/b

1 = 6√3/b /*b

b= 6√3

x= 6- 6√3

 

2)

ctg45 = a/y

ctg(45+15) = a/b

b= 2+y

 

1 = a/y

y=a

 

ctg60 = y/b

√3/3 = y/b

y = b *√3/3

 

y= (2+y)√3/3

y= 2√3/3 + y√3/3

y- y√3/3= 2√3/3

y (1- √3/3) =  2√3/3 /:(1- √3/3)

y = 2√3/3-√3

y= 2/(√3-1)

 

 

3) ctg30 = z/a

ctg60 = z/b

a = b-4

 

√3=z/a

a = z/√3

 

b=z/√3/3

b= √3z

 

z/√3=√3z - 4

z/√3 - √3z = -4 /*√3

z - 3z = -4√3

-2z = -2√3 /: -2

z = √3